2924: Pendulum Types

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Pendulum Types
The creepy fingers that grow from a vibrating cornstarch-water mix can be modeled as a chain of inverted vertical pendulums (DOI:10.1039/c4sm00265b) and are believed to be the fingers of Maxwell's Demon trying to push through into our universe.
Title text: The creepy fingers that grow from a vibrating cornstarch-water mix can be modeled as a chain of inverted vertical pendulums (DOI:10.1039/c4sm00265b) and are believed to be the fingers of Maxwell's Demon trying to push through into our universe.

Explanation[edit]

Ambox notice.png This explanation may be incomplete or incorrect: Embed animation of double pendulum crom wikipedia page.
If you can address this issue, please edit the page! Thanks.

This comic shows and describes several pendulums. The first three are actual physics models, while the last one is made up for absurdity. This is a recurring format of xkcd comics, as shown in 2289: Scenario 4.

The motion and dynamics of simple pendulum
The simple pendulum consists of a joint, rod, and weight, and when released (inside a gravity field or other accelerating force), it swings in a regular fashion. The "period" of a pendulum is the amount of time it takes to complete one cycle, swinging back and forth. In a simple pendulum, the period is consistent, predictable, and depends primarily on the length of the pendulum and the acceleration (being largely independent of both mass and length of arc). This predictability makes pendulums useful in applications such as timekeeping, where the earliest accurate clocks (such as a grandfather clock) made use of pendulums as regulators.


The typical motion of a double compound pendulum
The double pendulum consists of 2 joints, 2 rods, and a weight, and when released, it swings in a chaotic fashion. Interestingly, this follows by the mathematical definition of chaotic, being that small changes in initial conditions result in vast differences in end results. This pendulum is thus nearly unpredictable, and due to this chaotic nature, real life applications are very limited.


The inverted pendulum consists of a simple pendulum that is placed upside down, with some powered apparatus underneath vibrating it vertically to keep it upwards. If left unpowered it will fall, hence the "unstable" part. The comic appears to depict Kapitza's pendulum. See a video demonstration by Harvard Natural Sciences or an interactive simulation here.

The nightmare pendulum appears to be an inverted double pendulum, with an additional uninverted pendulum swinging within its much more substantial weight (which is also adorned with archaic/mystical symbols). The comic claims that this pendulum summons Maxwell's demon, jokingly implying that Maxwell’s demon is an actual entity. In fact, Maxwell's demon is a thought experiment in which a being - the demon -­­­­­ is posted at a tiny door between two gas vessels. It lets only slow-moving (cold) gas molecules move through the door in one direction, and only fast-moving (hot) ones in the other direction. One vessel gradually becomes hot and the other cold, violating the second law of thermodynamics. An actual machine doing that would require at least enough energy - in the form of information - so that no violation took place, but the thought experiment has stimulated much discussion since it was first proposed by James Clerk Maxwell in 1867.

The title text continues this joke explicitly, by referencing a real paper titled Vibro-levitation and inverted pendulum: parametric resonance in vibrating droplets and soft materials and implying that the paper ties the "creepy fingers" produced in this way to Maxwell's demon. The paper only actually suggests that the phenomenon is related to inverted pendulum dynamics. This gives a humorous example for the abuse of citations. Technically, the cited reference only supports the claim immediately before it, that the behavior of a cornstarch-water mix (also known as oobleck) can be modeled as inverted pendulums. But by proximity the reference also seems to support the part about Maxwell's demon. The illusion is helped by the description of the cornstarch as creepy, which is added in the beginning without any visible separation from the actual content of the citation.

Transcript[edit]

[Four types of pendulums are shown in a single panel. Each has a bullet list below the depiction.]
[Label:]
Simple pendulum
[A basic pendulum consisting of a joint, rod, and weight swinging in a regular arc]
  • Periodic
  • Stable
  • Useful for timekeeping
[Label:]
Double pendulum
[A pendulum consisting of 2 joints, 2 rods, and a weight swinging in a more loopy arc]
  • Aperiodic
  • Chaotic
  • Moderately cursed
[Label:]
Inverted pendulum
[An upside-down basic pendulum with some apparatus underneath vibrating up and down]
  • Finely balanced
  • Unstable
  • Becomes stable when vibrated
[Label:]
Nightmare pendulum
[An inverted double pendulum, with an additional uninverted pendulum swinging within a large weight adorned with archaic/mystical symbols]
  • Forbidden
  • Unphysical
  • Summons Maxwell's Demon


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Discussion

Example of the creepy fingers: https://youtu.be/3zoTKXXNQIU?si=MgZgSRFFyxrNGhw3 172.70.175.25 12:58, 24 April 2024 (UTC)

If that's as creepy as Maxwell's Demon gets, you have to wonder if he's related to Gachnar: https://www.facebook.com/watch/?v=3090746901188850 172.70.91.12 14:47, 24 April 2024 (UTC)

Fortunately, Maxwell's Demon can be banished with a silver hammer. 172.69.246.151 15:08, 24 April 2024 (UTC)

Is this a Dungeons and Discourse reference? Psychoticpotato (talk) 18:23, 24 April 2024 (UTC)
Ultimately that'd be from The Beatles... (Don't know that particular D'n'D thing, if that's a thing. Bet that's also a reference of its own.) 172.71.242.70 18:46, 24 April 2024 (UTC)
If by "Dungeons and Discourse", the webcomic from Dresden Codak is meant (two one-offs), it's not mentioned in those two strips (just Laplace's Demon). (Edit: I found Maxwell's demon (summonable, even), but not silver hammer, in this unofficial implementation of the game being played: https://web.archive.org/web/20220928185446/https://slatestarcodex.com/Stuff/DDThird_Edition.pdf) If, instead, the YouTube channel is meant, it doesn't seem like they review that level of content, based on the titles. 172.70.127.68 14:31, 5 May 2024 (UTC)

Thank you, whoever completed the transcript. I didn't know the bullet tag and the comics are starting to get more complicated to explain and transcribe. So again, my thanks. <3 Z1mp0st0rz (talk) 16:12, 24 April 2024 (UTC)

David Acheson showed that any finite number of inverted pendulum segments can be made stable through vibration. related video here: https://www.youtube.com/watch?v=BJ7_fFABc9s&t=0s 108.162.238.131 17:23, 24 April 2024 (UTC)

Considering that Maxwell's demon can reverse entropy, I welcome our new demon overlord. We must all put more starch onto speakers! Fabian42 (talk) 18:10, 24 April 2024 (UTC)

Summon Ba'al the Soul-Eater to rule beside Maxwell's Demon!!!!!!!!!!!!!!!! Z1mp0st0rz (talk) 19:22, 24 April 2024 (UTC)

Should we use "pendula" as the plural to "pendulum"? 172.70.110.47 (talk) 21:38, 24 April 2024 (please sign your comments with ~~~~)

The plural of pendulum would be penduli, as it is Latin second declension.172.70.42.128 13:31, 26 April 2024 (UTC)
Would it not still be pendula, because it is of the neutral gender?
I apologize. You are correct. I was thinking of the male gender. 172.70.135.51 13:11, 1 May 2024 (UTC)

Should we mention that Netflix's airing of 3-body problem means people are probably more interested in chaotic systems right now?--172.70.39.36 03:01, 25 April 2024 (UTC)

Plus there's the US elections coming up...162.158.95.97 09:09, 25 April 2024 (UTC)

A double pendulum requires 2 weights, and additional one at the center joint. Surprisingly Randal has that wrong. 172.69.60.177 00:25, 26 April 2024 (UTC)

Traditionally, I've seen that fudged by a massive 'link'. In fact, the two pendulum lengths can be dense bars, without even a terminating weight.
This obviously changes the dynamics, as the idealised pendulum has all its mass in the swinging weight at its end (the CoG in its centre), a swinging bar is 'twice as long as its swing-factor' (CoG is half way along). So a two-bar double-pendulum (assuming negligable weight bonus/deficit in the mid-joint mechanism) is a half-length-effect secondary pendulum sat at the end of an extended primary.
As if •-O-•-O-, •=joint (zero mass, zero size), -=extension (zero mass, zero flexibility), O=mass (zero size, zero flexibility)...). This is obviously differently 'tuned' to •—©—O (©=weight+joint, at a point).
...or else the inter-length joint, though not obviously so, is suitably overwhelmingly massive to do weight+jointing. 172.69.43.185 02:25, 26 April 2024 (UTC)
Two weights needed for a double pendulum [1]. As drawn, assuming a spherical cow in a vacuum, it's a simple pendulum, with two lightweight bars joined by a lightweight hinge, supporting one weight at a constant distance (as the hinge never bends) from the top support. -- Neil UK (talk) 16:53, 26 April 2024 (please sign your comments with ~~~~)

I wonder if Randall was playing Don’t Starve whose main antagonist is Maxwell, described as demonic, whose world is filled with nightmare themed contraptions, and which feature an entity called night hands that are creepy long fingers that come out at night to snatch your light. 162.158.158.234 (talk) 01:55, 26 April 2024 (please sign your comments with ~~~~)

Maxwell's Demon ultimately refers to a though experiment about entropy, and may very well be the inspiration for the Don't Starve character. However, here, it is most likely that he is referring to the thought experiment.172.70.42.129 13:40, 26 April 2024 (UTC)

There are white dots on the frame of the top piece of the Nightmare pendulum, but they aren't evenly spaced, which is indicative of ... something, maybe. Perhaps they are balls moving around a channel in the frame, to add to the chaos? 172.70.126.167 16:38, 26 April 2024 (UTC)

I would ALMOST take 5hem as markings, like a clock, but the gaps and the two close together at 4:30 makes me think you're right, they're balls rolling around further messing with the balance and adding to the chaos. NiceGuy1 (talk) 05:34, 28 April 2024 (UTC)

Maxwell's demon would indeed violate the laws of thermodynamics. If he was a real demon, i.e. was able to do the task effortless. --172.71.246.39 20:06, 1 May 2024 (UTC)